On September 30, 2016 all BTC-e accounts had to undergo the password changing procedure. BTC-e basically deactivated their users passwords and forced them to change them. Nothing complicated - just click link we send you to your e-mail you used for registration and you will be given new one. Some of you might already guess, I cant access my email - 2fa, cellphone lost and no chance to get back number that receives codes. When I try to recover my e-mail (googles says they usually respond within 3-5 days), nothing happens and I already wait like 2nd week. They just don't respond. Now, let me get to the point.

I asked btc-e to help me and they demand that in order to prove that I am the owner of said account, that I send deposit to my account from one of addresses used earlier to deposit coins to btc-e account I try to recover. Basically, I've send some bitcoins from my multibit hd wallet to my btc-e account, wallet generated address that has been used to send those coins and now they want me to send again some coins to my account from exactly same address. Is that possible? Whenever I try to send bitcoins, address is generated automatically and either there is no option to simply type address you want to use to send from or I am just too green.

You can only send from an address if it still has Bitcoin. Bitcoin is not actually stored in an address, and you can't just magically send from any address in your wallet. If you don't have any Bitcoin associated with an old address, you can't spend from it.

You should not need to send Bitcoin from an old address as you may not necessarily have money in an old address. You can however sign a message from an old address. Ask their support if they will accept a signed message (and they should, it still indicates that you control the private key to that address) and use that instead to prove ownership. Make sure your message also includes the current date and time when you sign it.

I actually did as you suggested Naoki earlier, and their answer was no. Since that leaves me only with gmail support as they still demand to make a deposit from same address as before and now remain silent, I'll think about making thread in accusation section regarding BTC-e if they will keep persist on that demand since, if I got it right, it is impossible to fulfill. Thank you for your time.

I actually did as you suggested Naoki earlier, and their answer was no. Since that leaves me only with gmail support as they still demand to make a deposit from same address as before and now remain silent, I'll think about making thread in accusation section regarding BTC-e if they will keep persist on that demand since, if I got it right, it is impossible to fulfill. Thank you for your time.

Mind elaborating on what exactly happened? Did you or did you not manage to send the coins as requested by them? This is the correct answer to the question in case of any doubt:

I was requested to send deposit from the same wallet and the same address I used to send myself the coins to my BTC-e acc. Since my wallet was pretty much empty, I purchased some coins from different exchange, send them from that exchange to my wallet and from my wallet to my account address at btc-e, so yes, I did made the deposit. Issue here is, BTC-e requires that I send this deposit from the same address I used earlier to deposit coins on their exchange, and when I did that, address from which the coins has been send was different (I can't or do not know how to send coins from address I used before, I was told it is pretty much not doable).